Aberration fields of off-axis astronomical telescopes induced by rotational misalignments.

Due to the absence of rotational symmetry, off-axis astronomical telescopes with off-set pupil become subject to rotational misalignments. Rotational misalignments of large off-axis mirrors with reference to their geometric center can greatly degrade the imaging quality. This paper presents an in-depth discussion on the net aberration fields of off-axis astronomical telescopes induced by rotational misalignments. Aberration function of off-axis telescopes with rotational misalignments is derived based on the framework of nodal aberration theory. Expressions of several important aberrations are obtained under some approximations. Then the specific field characteristics of these aberrations are presented and explicated. Meanwhile, we demonstrate that rotational misalignments can be converted to a kind of surface decenters; on the other hand, the effects of rotational misalignments have their special features which are different from the effects of general surface decenters. Besides, some other insightful discussions are further presented. This work is also applicable to the rotational misalignments of the off-axis segments of primary mirror in segmented mirror astronomical telescopes.